//---Robot dell'esempio 2, [CLO, p. 274]
//    con l2 = l3 = 1  e  1 <= l4 <= 2
//---Risolviamo il problema cinematico inverso, cioe'
//   dato il posizionamento della mano (a,b,c,s) = (2.5,0,1,0)
//   troviamo (c2,s2,c1,s1,l4)

ring r = 0,(c2,s2,c1,s1,l4),lp;
option(redSB);
ideal id=l4+(c1*c2-s1*s2)+c1-5/2,
(c1*s2+c2*s1)+s1,
c1^2+s1^2-1, c2^2+s2^2-1;
ideal gid = std(id);
dim(gid);
1
gid;
gid[1]=32*s1^2*l4-80*s1^2+8*l4^3-60*l4^2+118*l4-45
gid[2]=8*c1*l4-20*c1+4*l4^2-20*l4+25
gid[3]=c1^2+s1^2-1
gid[4]=2*s2-2*s1*l4+5*s1
gid[5]=8*c2-4*l4^2+20*l4-17
//---non c'e' il tempo per discutere il sistema
//---poniamo  l4 = 1.5
ideal ids = subst(id, l4, 3/2);
ids;
ids[1]=c2*c1-s2*s1+c1-1
ids[2]=c2*s1+s2*c1+s1
ids[3]=c1^2+s1^2-1
ids[4]=c2^2+s2^2-1
ring r2 = 0,(c2,s2,c1,s1),lp;
ideal ids2 = imap(r,ids);
ids2;
ids2[1]=c2*c1-s2*s1+c1-1
ids2[2]=c2*s1+s2*c1+s1
ids2[3]=c1^2+s1^2-1
ids2[4]=c2^2+s2^2-1
LIB "solve.lib";
// ** loaded /usr/bin/../share/singular/LIB/solve.lib (4.0.0.0,Jun_2013)
// ** loaded /usr/bin/../share/singular/LIB/ring.lib (4.0.0.0,Jun_2013)
// ** loaded /usr/bin/../share/singular/LIB/primdec.lib (4.0.1.2,Jan_2015)
// ** loaded /usr/bin/../share/singular/LIB/absfact.lib (4.0.0.0,Jun_2013)
// ** loaded /usr/bin/../share/singular/LIB/matrix.lib (4.0.0.0,Jun_2013)
// ** loaded /usr/bin/../share/singular/LIB/nctools.lib (4.0.0.0,Jun_2013)
// ** loaded /usr/bin/../share/singular/LIB/random.lib (4.0.0.0,Jun_2013)
// ** loaded /usr/bin/../share/singular/LIB/poly.lib (4.0.0.0,Jun_2013)
// ** loaded /usr/bin/../share/singular/LIB/elim.lib (4.0.0.1,Jan_2014)
// ** loaded /usr/bin/../share/singular/LIB/general.lib (4.0.0.1,Jan_2014)
// ** loaded /usr/bin/../share/singular/LIB/inout.lib (4.0.0.0,Jun_2013)
// ** loaded /usr/bin/../share/singular/LIB/triang.lib (4.0.0.0,Jun_2013)
list l=solve(ids2,6,0);
[1]:
   [1]:
      -0.5
   [2]:
      0.866025
   [3]:
      0.5
   [4]:
      -0.866025
[2]:
   [1]:
      -0.5
   [2]:
      -0.866025
   [3]:
      0.5
   [4]:
      0.866025

// 'solve' created a ring, in which a list SOL of numbers (the complex solutions)
// is stored.
// To access the list of complex solutions, type (if the name R was assigned
// to the return value):
        setring R; SOL; 
monitor("");